Radial Wave Function

$u(r)\equiv rR(r)\to -\frac{{\hslash }^2}{2m}\frac{{\mathrm{d}}^{2}u}{\mathrm{d}{r}^2}+V_{\text{effective}}u=Eu$

• Radial equation which may be used to solve for $R(r)$, the radial wave function

$V_{\text{effective}}=V+\frac{{\hslash }^2}{2m}\frac{l(l+1)}{r^2}$

• The second term is called the centrifugal term, which has the effect of pushing the particle away from the origin